%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE128+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:58:54 PM UTC 2026
% Result : Theorem 0.13s 10.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 35 unt; 0 def)
% Number of atoms : 54 ( 53 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 8 ~; 4 |; 2 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 1 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(forward_diamond,axiom,
! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(divergence2,axiom,
! [X4,X5,X6] :
( addition(domain(X4),addition(forward_diamond(X5,domain(X4)),domain(X6))) = addition(forward_diamond(X5,domain(X4)),domain(X6))
=> addition(domain(X4),addition(divergence(X5),forward_diamond(star(X5),domain(X6)))) = addition(divergence(X5),forward_diamond(star(X5),domain(X6))) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+7.ax',divergence2) ).
fof(goals,conjecture,
! [X4] :
( divergence(X4) = zero
=> ! [X5] :
( addition(domain(X5),forward_diamond(X4,domain(X5))) = forward_diamond(X4,domain(X5))
=> domain(X5) = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(c_0_10,plain,
! [X42,X43] : forward_diamond(X42,X43) = domain(multiplication(X42,domain(X43))),
inference(variable_rename,[status(thm)],[forward_diamond]) ).
fof(c_0_11,plain,
! [X33] : domain(X33) = antidomain(antidomain(X33)),
inference(variable_rename,[status(thm)],[domain4]) ).
fof(c_0_12,plain,
! [X32] : addition(antidomain(antidomain(X32)),antidomain(X32)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_13,plain,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_14,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_15,plain,
! [X29] : multiplication(antidomain(X29),X29) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_16,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_17,plain,
! [X51,X52,X53] :
( addition(domain(X51),addition(divergence(X52),forward_diamond(star(X52),domain(X53)))) = addition(divergence(X52),forward_diamond(star(X52),domain(X53)))
| addition(domain(X51),addition(forward_diamond(X52,domain(X51)),domain(X53))) != addition(forward_diamond(X52,domain(X51)),domain(X53)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[divergence2])])]) ).
cnf(c_0_18,plain,
forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_25,negated_conjecture,
~ ! [X4] :
( divergence(X4) = zero
=> ! [X5] :
( addition(domain(X5),forward_diamond(X4,domain(X5))) = forward_diamond(X4,domain(X5))
=> domain(X5) = zero ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_26,plain,
( addition(domain(X1),addition(forward_diamond(X2,domain(X1)),domain(X3))) != addition(forward_diamond(X2,domain(X1)),domain(X3))
| addition(domain(X1),addition(divergence(X2),forward_diamond(star(X2),domain(X3)))) = addition(divergence(X2),forward_diamond(star(X2),domain(X3))) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
forward_diamond(X1,X2) = antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_19]) ).
cnf(c_0_28,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
fof(c_0_31,plain,
! [X25] : multiplication(X25,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
fof(c_0_32,negated_conjecture,
( domain(esk2_0) != zero
& addition(domain(esk2_0),forward_diamond(esk1_0,domain(esk2_0))) = forward_diamond(esk1_0,domain(esk2_0))
& divergence(esk1_0) = zero ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])]) ).
cnf(c_0_33,plain,
( addition(antidomain(antidomain(X1)),addition(antidomain(antidomain(multiplication(X2,antidomain(antidomain(antidomain(antidomain(X1))))))),antidomain(antidomain(X3)))) != addition(antidomain(antidomain(multiplication(X2,antidomain(antidomain(antidomain(antidomain(X1))))))),antidomain(antidomain(X3)))
| addition(antidomain(antidomain(X1)),addition(divergence(X2),antidomain(antidomain(multiplication(star(X2),antidomain(antidomain(antidomain(antidomain(X3))))))))) = addition(divergence(X2),antidomain(antidomain(multiplication(star(X2),antidomain(antidomain(antidomain(antidomain(X3)))))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_27]),c_0_27]),c_0_27]),c_0_27]) ).
cnf(c_0_34,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_35,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,negated_conjecture,
addition(domain(esk2_0),forward_diamond(esk1_0,domain(esk2_0))) = forward_diamond(esk1_0,domain(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,negated_conjecture,
domain(esk2_0) != zero,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
( addition(antidomain(antidomain(X1)),antidomain(antidomain(multiplication(X2,antidomain(antidomain(antidomain(antidomain(X1)))))))) != antidomain(antidomain(multiplication(X2,antidomain(antidomain(antidomain(antidomain(X1)))))))
| addition(antidomain(antidomain(X1)),divergence(X2)) = divergence(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29]),c_0_34]),c_0_29]),c_0_35]),c_0_34]),c_0_29]),c_0_24]),c_0_29]),c_0_34]),c_0_29]),c_0_35]),c_0_34]),c_0_29]),c_0_24]),c_0_29]),c_0_24]),c_0_29]),c_0_24]) ).
cnf(c_0_39,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0)))))))) = antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_19]),c_0_19]),c_0_19]),c_0_27]),c_0_27]) ).
cnf(c_0_40,negated_conjecture,
divergence(esk1_0) = zero,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,negated_conjecture,
antidomain(antidomain(esk2_0)) != zero,
inference(rw,[status(thm)],[c_0_37,c_0_19]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_24]),c_0_40]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE128+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/10.37 % Computer : n011.cluster.edu
% 0.08/10.37 % Model : x86_64 x86_64
% 0.08/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.37 % Memory : 8046.5625MB
% 0.08/10.37 % OS : Linux 6.8.0-71-generic
% 0.08/10.37 % CPULimit : 300
% 0.08/10.37 % WCLimit : 300
% 0.08/10.37 % DateTime : Sun Sep 20 22:45:36 UTC 2026
% 0.08/10.37 % CPUTime :
% 0.08/10.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/10.41 Running first-order theorem proving
% 0.13/10.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/10.45 % Version: 3.5.1
% 0.13/10.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/10.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/10.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/10.45 % Starting new_bool_3 with 300s (1) cores
% 0.13/10.45 % Starting new_bool_1 with 300s (1) cores
% 0.13/10.45 % Starting sh5l with 300s (1) cores
% 0.13/10.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 354080 completed with status 0
% 0.13/10.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/10.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/10.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/10.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/10.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/10.45 % No SInE strategy applied
% 0.13/10.45 % Search class: FHUSM-FFMF21-DFFFFFNN
% 0.13/10.45 % partial match(1): FHUSM-FFMF21-MFFFFFNN
% 0.13/10.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/10.45 % Starting SubtermCWHack with 136s (1) cores
% 0.13/10.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/10.45 % Starting G-E--_100_C18_F1_PI_AE_Q4_CS_SP_S0Y with 212s (1) cores
% 0.13/10.45 % Starting H----_042_B03_F1_AE_Q4_SP_S2S with 136s (1) cores
% 0.13/10.45 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 0.13/10.45 % G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 354091 completed with status 0
% 0.13/10.45 % Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 0.13/10.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/10.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/10.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/10.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/10.45 % No SInE strategy applied
% 0.13/10.45 % Search class: FHUSM-FFMF21-DFFFFFNN
% 0.13/10.45 % partial match(1): FHUSM-FFMF21-MFFFFFNN
% 0.13/10.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/10.45 % Starting SubtermCWHack with 136s (1) cores
% 0.13/10.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/10.45 % Starting G-E--_100_C18_F1_PI_AE_Q4_CS_SP_S0Y with 212s (1) cores
% 0.13/10.45 % Starting H----_042_B03_F1_AE_Q4_SP_S2S with 136s (1) cores
% 0.13/10.45 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 0.13/10.45 % Preprocessing time : 0.002 s
% 0.13/10.45 % Presaturation interreduction done
% 0.13/10.45
% 0.13/10.45 % Proof found!
% 0.13/10.45 % SZS status Theorem
% 0.13/10.45 % SZS output start CNFRefutation
% See solution above
% 0.13/10.45 % Parsed axioms : 29
% 0.13/10.45 % Removed by relevancy pruning/SinE : 0
% 0.13/10.45 % Initial clauses : 32
% 0.13/10.45 % Removed in clause preprocessing : 8
% 0.13/10.45 % Initial clauses in saturation : 24
% 0.13/10.45 % Processed clauses : 101
% 0.13/10.45 % ...of these trivial : 20
% 0.13/10.45 % ...subsumed : 0
% 0.13/10.45 % ...remaining for further processing : 81
% 0.13/10.45 % Other redundant clauses eliminated : 0
% 0.13/10.45 % Clauses deleted for lack of memory : 0
% 0.13/10.45 % Backward-subsumed : 0
% 0.13/10.45 % Backward-rewritten : 4
% 0.13/10.45 % Generated clauses : 552
% 0.13/10.45 % ...of the previous two non-redundant : 297
% 0.13/10.45 % ...aggressively subsumed : 0
% 0.13/10.45 % Contextual simplify-reflections : 0
% 0.13/10.45 % Paramodulations : 552
% 0.13/10.45 % Factorizations : 0
% 0.13/10.45 % NegExts : 0
% 0.13/10.45 % Equation resolutions : 0
% 0.13/10.45 % Disequality decompositions : 0
% 0.13/10.45 % Total rewrite steps : 1145
% 0.13/10.45 % ...of those cached : 909
% 0.13/10.45 % Propositional unsat checks : 0
% 0.13/10.45 % Propositional check models : 0
% 0.13/10.45 % Propositional check unsatisfiable : 0
% 0.13/10.45 % Propositional clauses : 0
% 0.13/10.45 % Propositional clauses after purity: 0
% 0.13/10.45 % Propositional unsat core size : 0
% 0.13/10.45 % Propositional preprocessing time : 0.000
% 0.13/10.45 % Propositional encoding time : 0.000
% 0.13/10.45 % Propositional solver time : 0.000
% 0.13/10.45 % Success case prop preproc time : 0.000
% 0.13/10.45 % Success case prop encoding time : 0.000
% 0.13/10.45 % Success case prop solver time : 0.000
% 0.13/10.45 % Current number of processed clauses : 53
% 0.13/10.45 % Positive orientable unit clauses : 47
% 0.13/10.45 % Positive unorientable unit clauses: 1
% 0.13/10.45 % Negative unit clauses : 1
% 0.13/10.45 % Non-unit-clauses : 4
% 0.13/10.45 % Current number of unprocessed clauses: 218
% 0.13/10.45 % ...number of literals in the above : 258
% 0.13/10.45 % Current number of archived formulas : 0
% 0.13/10.45 % Current number of archived clauses : 36
% 0.13/10.45 % Clause-clause subsumption calls (NU) : 1
% 0.13/10.45 % Rec. Clause-clause subsumption calls : 1
% 0.13/10.45 % Non-unit clause-clause subsumptions : 0
% 0.13/10.45 % Unit Clause-clause subsumption calls : 3
% 0.13/10.45 % Rewrite failures with RHS unbound : 0
% 0.13/10.45 % BW rewrite match attempts : 38
% 0.13/10.45 % BW rewrite match successes : 25
% 0.13/10.45 % Condensation attempts : 0
% 0.13/10.45 % Condensation successes : 0
% 0.13/10.45 % Termbank termtop insertions : 9149
% 0.13/10.45 % Search garbage collected termcells : 74
% 0.13/10.45
% 0.13/10.45 % -------------------------------------------------
% 0.13/10.45 % User time : 0.011 s
% 0.13/10.45 % System time : 0.005 s
% 0.13/10.45 % Total time : 0.016 s
% 0.13/10.45 % Maximum resident set size: 3664 pages
% 0.13/10.45
% 0.13/10.45 % -------------------------------------------------
% 0.13/10.45 % User time : 0.057 s
% 0.13/10.45 % System time : 0.017 s
% 0.13/10.45 % Total time : 0.074 s
% 0.13/10.45 % Maximum resident set size: 4864 pages
% 0.13/10.45 % E exiting
%------------------------------------------------------------------------------